We have so far, derived several different models and now comes the time to compare

them, specifically in terms of their frequency range of validity.

Let us review the values models we have derived.

The first was the simple model that was, claimed to be valid up to medium

frequencies. It includes a constant trans-conductance

GM, and a few capacitance's, five of them.

Then we derive the complete quasi-static model which can be though of as resulting

from this with addition of certain elements.

Of particular interest, is this element here, a new control source, it is

controlled by VGS but, the derivative of VGS appears here and it appears in

parallel with the GM VGS source. We have already mentioned that in the

frequency domain, this converts to J omega CM VGS, so therefore, the combined

current of these two sources is GM minus J Omega CM times VGS.

And the minus appears because this direction is opposite from this

direction. Finally, we had the non quasi-static

model. First order non quasi-static model, which

again, can be thought of as resulting from these after adding certain elements,

like series resistors and inductor over here, all coming out of the math.

And instead of a constant trans conductance GM, we have a trans

admittance that has one plus J Omega tau one, where tau one depends on the

operating point in the denominator. And we have seen, that as omega goes up,

the tau centimeters goes down, which is a manifestation of the fact that at very

high frequencies, the device gives up. So, we have these three models and we

would like now to compare them. To do a complete job would take a very

long time, so what I will do is I will concentrate on the trans admittance of

the three elements, of the three models. And compare it versus frequency for one

specific operating point. And the operating point I will assume

that is that we are somewhere in the middle between VDS equal zero and VDS

equal to VDS prime. In other words, we're in the middle of

the non saturation region. So, the first model, which is the simple

model, has a constant trans conductance times VGS, and this is the control

current source that tells you how much the drain current will vary when you vary

a drift, the gate source voltage, VGS. The complete quasi-static model has, in

addition to the GM VGS, a control source, a J Omega CMVGS source going in the

opposite direction, and the resulting trans admittance is GM minus J Omega CM.

If you multiply this trans admittance by VGS, you get the current which is the sum

of the two currents taking the different direction of the current sources into

account. The third model is the non-quasi static

model which had the transmittance in lieu of the trans conductance, and it is GM

over one plus J Omega tau one VGS. And the fourth model we will consider is

a high order model. We have not derived this, but it can be

derived, and it is done in the literature.

You can find references in the book. Now, if you plot these parameters versus

frequency, both magnitude and phase you find these results.